Answer
$104$
Work Step by Step
Consider $I_0= \int_0^{2\pi} \int_{2x}^{4} (x^2+y^2) (3) \ dy \ dx$
or, $= 3 \int_0^{2} (4x^2 +\dfrac{64}{3}-\dfrac{14x^3}{3}) \ dx$
or, $=3 [\dfrac{4x^3}{3}+\dfrac{64x}{3}-\dfrac{14x^4}{12}]
_0^2 $
or, $=3 [\dfrac{4(2^3-0)}{3}+\dfrac{64(2-0)}{3}-\dfrac{14(2^4-0)}{12}]$
or, $=104$
